The Least Absolute Shrinkage and Selection Operator (LASSO) method introduced by R. Tibshirani [1]} is a highly successful technique for feature selection in machine learning that has found additional applications in compressive sampling recovery [2]} and system identification [3]}.
A generalization by M. Yuan and Y. Lin [4]} called group LASSO is especially relevant for sensor placement since it allows measurements to be selected in groups that might come from the same sensor at different instants of time.
Suppose we are given a collection of data consisting of available measurements \({\mathbf {m}}_j({\mathbf {x}}_i)\) , \(j=1,\ldots ,M\)  along with relevant quantities \({\mathbf {g}}({\mathbf {x}}_i)\)  that we wish to reconstruct over a collection of states \({\mathbf {x}}_i\) , \(i=1,\ldots ,N\) . The group LASSO convex optimization problem takes the form
\(\operatornamewithlimits{\min \!imize}_{{\mathbf {A}}_1, \ldots , {\mathbf {A}}_M} \sum _{i=1}^N\Big \Vert {\mathbf {g}}({\mathbf {x}}_i) - \sum _{j=1}^M{\mathbf {A}}_j{\mathbf {m}}_j({\mathbf {x}}_i) \Big \Vert _2^2 + \gamma \sum _{j=1}^M \left\Vert {\mathbf {A}}_j \right\Vert _F\) 
